Grid Classes and the Fibonacci Dichotomy for Restricted Permutations

We introduce and characterise grid classes, which are natural generalisations of other well-studied permutation classes. This characterisation allows us to give a new, short proof of the Fibonacci dichotomy: the number of permutations of length n in a permutation class is either at least as large as the nth Fibonacci number or is eventually polynomial.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Sophie Huczynska, Vincent Vatter
• Keywords: COMBINATORICS 2006, Nth Fibonacci Number, Permutation, Well-studied Permutation Classes